A standard cup holder of the type used in a motor vehicle, although of course suitable for use elsewhere such as on a golf pull cart, typically has an upwardly open cup-shaped seat dimensioned to hold the largest normally encountered cup or beverage container. When a large beverage container, such as a 20-oz soda bottle, is set in it, the fit is fairly good and the beverage container is solidly held. When, however, a smaller-diameter container or a tapered container is set in such a cup holder, it is fairly loose and can wobble from side to side as the vehicle moves, spilling or even allowing the beverage container to hop out of the holder.